A129487 Unitary deficient numbers.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79

Offset: 1

Author

Ant King, Apr 20 2007

Keywords

• easy
• nonn

Comments

The unitary deficient numbers account for almost 93% of all integers (including all primes (A000040) and prime powers (A000961)) and asymptotically satisfy a(n)~1.0753n. This provides an excellent fit as n grows larger. For example, the one millionth unitary deficient number is 1075293 and the asserted approximation returns 1075300, giving an error of only 0.00065%.

Examples

			The sixth integer that exceeds the sum of its proper unitary divisors is 7. Hence a(6)=7.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034460, A034448, A129468, A034683, A000040, A000961.

Programs

Maple

a := proc(n) numtheory[divisors](n); select(d -> igcd(d,n/d)=1,%); `if`(add(i,i=%) < 2*n,n,NULL) end: # Peter Luschny, May 03 2009

Mathematica

UnitaryDivisors[n_Integer?Positive]:=Select[Divisors[n],GCD[ #,n/# ]==1&];Select[Range[100],Plus@@UnitaryDivisors[ # ]-2#<0 &]

Formula

Integers for which A034460(n) < n, or equivalently for which A034448(n) < 2n.